Given a large integer data set shared vertically by two parties, we consider the problem of securely computing a score separating the k{\rm th} and the (k + 1){\rm th} element. An efficient secure protocol is developed to compute such a score while revealing little additional information. The proposed protocol is implemented using the Fairplay system and experimental results are reported. We show a real application of this protocol as a component used in the secure processing of top-k queries over vertically partitioned data.